Martin was born in Birmingham, Alabama, the son of Ellie Gordon (Robinson) and Hugh Martin, Sr., an architect. He attended Birmingham-Southern College where he studied music.
He was a member of the Beta Beta Chapter of the Alpha Tau Omega fraternity.
Martin wrote the music, and in some cases the lyrics, for five Broadway musicals: Best Foot Forward (1941); Look Ma, I'm Dancin'! (1948); Make a Wish (1951); High Spirits (1964) (music and lyrics, with Timothy Gray); and Meet Me In St. Louis (1989), a stage version of the film with an expanded score by Martin and Ralph Blane. He also composed the songs for the West End musical Love from Judy (1952).
Martin's first Broadway credit was as an arranger for the 1937-1938 musical Hooray for What! and was a vocal or choral arranger for such later Broadway musicals as The Boys From Syracuse (1938–39), Too Many Girls (1939–40), DuBarry Was a Lady (1939–40), Cabin in the Sky (1940–41), and Gentlemen Prefer Blondes (1949–51), Top Banana (1951–52), and Lorelei (1974). He was a vocal arranger for Sugar Babies (1979–82).
As a performer, Martin appeared on Broadway in Hooray for What! (1937), Where Do We Go From Here (1938), and Louisiana Purchase (1940–41).
Ralph Blane was Martin's songwriting partner for most of his work, and the two recorded an album of their songs entitled Martin and Blane Sing Martin and Blane with the Ralph Burns Orchestra in 1956. Martin and Blane were twice nominated for the Academy Award for Best Song, for "The Trolley Song" in 1944, and for "Pass That Peace Pipe" (co-written by Roger Edens) from Good News in 1947. Hugh Martin also received four Tony Award nominations, three for High Spirits (Best Musical, Best Book Author of a Musical, Best Composer and Lyricist) and one for the 1990 Meet Me in St. Louis (Best Original Score).
Martin's other film work included songs for the films Athena (1954) starring Jane Powell, Debbie Reynolds, and Vic Damone, and The Girl Most Likely (1957) starring Jane Powell as well as the film version of his Broadway hit Best Foot Forward (1943) which starred Lucille Ball.
Martin collaborated with vocalist Michael Feinstein for a 1995 CD Michael Feinstein Sings The Hugh Martin Songbook, an album on which the then 80-year-old songwriter accompanied Feinstein on piano and sang a duet. On an earlier CD Feinstein recorded the memorable Martin composition, "On Such a Night as This". He also released an album of his music called Hugh Sings Martin on the record label PS Classics, which drew from his catalog as a composer, lyricist, arranger and singer. The album was released in conjunction with the Library of Congress.
Martin, a Seventh-day Adventist, spent much of the 1980s as an accompanist for gospel female vocalist Del Delker on her revival tours and in 2001 rewrote his most famous song (with the assistance of Garland biographer John Fricke) as a more specifically religious number, "Have Yourself A Blessed Little Christmas", which was recorded that year by Delker with the 86-year-old songwriter playing piano on the recording.
Although Ralph Blane is credited with writing the music for many of Martin's songs, Martin claimed in his autobiography that he wrote both music and lyrics to all of the songs in Meet Me In St. Louis and that "all of the so-called Martin and Blane songs, (except for "Buckle Down, Winsocki" in Best Foot Forward), were written entirely by me (solo) without help from Ralph or anybody else." His explanation for allowing Blane equal credit for the songs was explained, "I was reasonably content to let him receive equal screen credit, sheet music credit, ASCAP royalties, etc., mainly because this bizarre situation was caused by my naive and atrocious lack of business acumen."
Martin was the subject of a songbook collection, The Songs of Hugh Martin published by Hal Leonard Publishing in 2008. He published his autobiography Hugh Martin - The Boy Next Door in October 2010 at age 96. Martin was a member of the Songwriters Hall of Fame and Alabama Music Hall of Fame and lived in Encinitas, California.
Martin died on March 11, 2011 in Encinitas, California at age ninety-six.